Particles, Waves and Trajectories: 210 Years After Young’s Experiment

The success of quantum mechanics to explain the physical world is indisputable. This ranges from very fundamental aspects to technological applications that are currently part of our daily life. But, what do we know about the quantum world itself? The answer to this question is unclear, since quantum mechanics is still a mystery at a deeper level of understanding. Nothing precise can be said about quantum systems (regardless of what we may mean by a quantum system), but probabilistic. What is more, complementary properties cannot be measured at the same time, as Young’s celebrated two-slit experiment nicely shows.

As an important consequence of this fact, the notion of well-defined trajectory has been proscribed in quantum descriptions due to a conceptual rather than physical incompatibility between this concept and the wave-like behavior of quantum systems. Bohmian mechanics goes beyond such prejudices, allowing us to understand the individual evolution of quantum systems, while keeping a formal equivalence with standard quantum mechanics in the statistical limit (i.e., when carrying out a sampling over many realizations for such systems or, equivalently, many identical systems). Actually, the key idea of this hydrodynamic reformulation of quantum mechanics is easily transferable to other physical contexts where waves (or distributions) are the primary descriptor, thus establishing an interesting link between quantum mechanics and any other wave theory. Even though the nature of the waves involved in these theories may be very different, the general way how all these theories operate is, in essence, still the same –same type of concepts (e.g., coherence, interference, diffraction, tunneling, discreteness, etc.) and principles (e.g., uncertainty, superposition).

In this communication, an overview of how the concept of trajectory or streamline has been used in different contexts as a tool to analyze, to understand, and to provide alternative pictures of processes and phenomena will be presented. This feeling (or way to proceed) can be traced back to Madelung’s 1926 hydrodynamic approach (a synonymous of Bohmian mechanics), although it has received less attention in the literature than de Broglie’s or Bohm’s approaches. Then, the discussion will turn to the analysis of three particular problems: (1) dissipation in the context of the Caldirola-Kanai model, (2) frequency analysis of time-dependent processes, and (3) the gap between single-photon detections and Maxwell’s electromagnetism.